Journal of the
Korean Mathematical Society JKMS

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder\'{o}n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

Keywords: nonlinear elliptic equation, global gradient estimate, Calder\'{o}n-Zygmund theory, BMO space, Reifenberg flat domain

MSC numbers: 35J60, 46E30